You will probably have a wireless router connected to the 'phone line.
You can connect to the router either wirelessly (usual) or by a cable (unusual).
Your second machine either needs a network card and a cable or more preferably a wireless card and the device driver software to make it work.
My BT router manages up to 7 connections from different machines - all wireless - but seldom more than 4 at a time.
Use Control Panel Network Connections to set up the local network between computer and router. Right click on the wireless icon and select View Available Wireless Networks - you may see several neighbourhood routers - select and connect to your own.
Good luck...
Peccavi
June 2009